Chaos Behavior Research Articles

Chaotic or crowded? The role of physical household environment in children's learning during the COVID-19 pandemic

Household chaos and crowding are known to significantly influence children's development; however, their relative contributions remain less clear. Furthermore, previous research has primarily focused on children's socioemotional and cognitive development, with limited attention to the learning process. This study explores the relation of household chaos and crowding with children's learning behaviors and emotions during the COVID-19 pandemic in Hong Kong. A sample of 262 parents and their primary school-aged children were recruited in Hong Kong. Both parents and children completed separate online questionnaires. Structural equation modeling revealed that while household chaos was correlated with crowding, it was specifically chaos, rather than crowding, that negatively related to children's learning behaviors. Importantly, the direct relationship between household chaos and children's learning behaviors remained significant even after accounting for family socioeconomic status (SES) and parents' involvement. This study enhances our understanding of the relation of physical environment with children's learning, emphasizing the distinct role of household chaos, separate from crowding and family SES.

Nonlinear behavior and energy harvesting performance of a new tunable quasi-zero stiffness system.

Energy harvesting from vibrations is a popular research topic. However, it is difficult to change the values of its dynamic stiffness characteristics during the operation of device. This paper analyzes the nonlinear dynamical behavior and energy harvesting performance of an energy harvesting device with a gear unit and an inertial amplifier. The Melnikov method is used to discriminate the chaos behavior of the system and is illustrated by numerical simulations. Chaotic dynamics analysis provides a simplified analytical idea that offers more insight into the performance of this energy harvesting device. In addition, the basins of attraction of the coexistence solution of the system are plotted, and the trajectory and energy harvesting efficiency of the system are analyzed for changes in the initial value. The results show that the device has the convenience to change the form and efficiency of system energy harvesting. The theory of Melnikov functions recognizes the presence of chaos and can provide solutions for the parameterization of the system. The choice of initial value greatly affects the energy harvesting efficiency.

The experimental research of which different types of impact signals affect the bifurcation chaos behavior of three-degree-of-freedom collision system

Abstract Collision is a faulty behavior in mechanical equipment, which greatly affects the safety of equipment. In this paper, aiming at the collision failures that are prone to occur in mechanical equipment, the nonlinear fault collision behavior of a class of three-degree-of-freedom collision systems is studied. A three-degree-of-freedom piecewise non-smooth collision experiment platform system has been established to facilitate further analysis of the bifurcations and chaos inherent to the bearings system. This analysis is conducted through the use of Poincaré mapping on the collision plane. The excitation signals employed, which include sinusoidal, triangular, and rectangular signals, result in the emergence of specific types and orders of bifurcation behaviours within the system, as evidenced by the establishment of a Poincaré mapping at the collision surface, and this is observed to occur as the vibration frequency increases. The characteristics of impact signals generated by force sensors and the influence of impact signal type on the system are investigated. The nonlinear impact behavior of three-degree-of-freedom collision systems provides a reliable foundation for the design, fault diagnosis, and theoretical guidance of large-scale high-speed rotating machinery, as well as technical support for safe and stable operation of high-speed rotating machinery, which is essential for failure analysis and vibration reduction in equipment.

A novel memristive chaotic jerk circuit and its microcontroller-based sliding mode control

Due to the experimental realization of memristor circuit elements, research on memristors and memristor-based circuits has surged. Because of their nonvolatile and nonlinear behavior, memristors can be easily applied to chaotic circuits. This study introduces a novel memristive 3D chaotic jerk system, comprising only seven terms, along with its electronic model and microcontroller-based control. The flux-controlled memristor-based jerk system exhibits complex dynamics, which were analyzed through various properties such as phase portraits, the Jacobian matrix, equilibria, eigenvalues, Lyapunov spectra, bifurcation diagrams, and transient chaos behavior. Three controllers, namely, nonlinear feedback, classical sliding mode, and integral sliding mode were designed to control the chaotic jerk oscillator. Lyapunov functions were used to synthesize the nonlinear feedback controller and ensure system stability with the sliding mode technique. Numerical tests under various performance criteria and disturbance conditions showed that the sliding mode controller outperforms the nonlinear feedback controller due to its single-state control structure. The chaotic jerk oscillator hardware circuit was designed and implemented, operating easily with initial conditions set to zero and low DC supply voltages, with all output voltages within ±6V. Both theoretical and simulation results demonstrate the system’s complexity and applicability, with experimental results aligning well with simulations. Consequently, effective microcontroller-based control was achieved using a single-state controller.

Chaos, synchronization, and emergent behaviors in memristive hopfield networks: bi-neuron and regular topology analysis

Chaos, synchronization, and emergent behaviors in memristive hopfield networks: bi-neuron and regular topology analysis

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior

This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system’s behavior and the extent to which it deviates from the unperturbed case.

Household chaos and child problem behaviors: A cross-cultural examination of the mediating and moderating role of mindful parenting.

Household chaos has been shown to adversely associate with children's behavioral adjustment. However, the mechanism underlying the relationship between household chaos and children's behaviors is not yet fully understood. The current study proposes mindful parenting as an important mediating and moderating factor in the relationship between household chaos and child problem behaviors. This study also examines cultural influences in this process, comparing the UK and Türkiye, considering both mothers' and children's perspectives on mindful parenting. Cross-sectional questionnaires were administered to mothers and their children aged 11-16 years in the UK (n = 90; 53.3% girl) and Türkiye (n = 154; 54.5% girl) in 2021. Mother reports of the Confusion, Hubbub, and Order Scale and the Strengths and Difficulties Questionnaire, as well as mother and child reports of Mindful Parenting Inventories for Parents (MPIP) and Children (MPIC), were used to assess household chaos, child problem behaviors, and mindful parenting, respectively. Multiple-group path analysis revealed that household chaos was a significant indirect predictor of child problem behaviors via mindful parenting in both countries. Furthermore, simple slopes analysis showed that mindful parenting moderated the link between household chaos and child problem behaviors in the UK. Overall, our study sheds light on the importance of micro- and macro-environmental factors and their interactions in children's adjustment.

Appearance of transient chaos and energy variability in Ueda oscillator driven by an amplitude‐modulated force

Transient chaos is a characteristic behavior observed in nonlinear systems, where trajectories within a specific region of phase space exhibit chaotic dynamics for a finite duration before transitioning to an external attractor. In many nonlinear systems, transient and chaotic behaviors are closely associated with variations in the system's energy. In this paper, we introduce the concept of an energy variable and establish its connection with the Melnikov integral. We explore the influence of energy variation in an amplitude‐modulated (AM) force‐driven Ueda oscillator through numerical simulations. Our investigation reveals the emergence of transient chaos, chaotic dynamics, and regular behaviors, underscoring the significant role played by the energy variable, denoted as , in the system. We employ various analytical tools, including phase diagrams, Poincaré maps, time series plots, and bifurcation diagrams, to characterize and visualize transient chaos, regular, and chaotic motions within the system.

Preschoolers' Self-Regulation and Behavior Problems in the Midst of Caregiver Depression and Chaos.

Preschoolers' self-regulation is partially developed through home and child care routines. COVID-19-related child care closures increased caregiver depressive symptoms, household chaos, and children's behavior problems. This longitudinal study examined how preschoolers' prepandemic self-regulation was related to behavior problems early in the pandemic, including buffering against the adverse effects of caregiver depressive symptoms and household chaos. A sample of 264 caregivers of preschoolers reported on their children's self-regulation (Behavior Rating Inventory of Executive Function-Preschool Version Inhibitory Self Control Index) before the pandemic and caregiver depressive symptoms (Center for Epidemiological Studies), household chaos (Confusion, Hubbub, and Order Scale), and children's behavior problems (Behavior Rating Index for Children) during the pandemic. We used linear mixed models to examine predictors of children's behavior problems, including prepandemic self-regulation, and further examined moderation by pandemic-related caregiver depressive symptoms and household chaos. Children were 64% non-Hispanic White and 24% non-Hispanic Black, with mean pandemic age 5.9 years. Prepandemic self-regulation significantly predicted early pandemic behavior problems (β = -0.38 [95% confidence interval, -0.69 to -0.07]). This association was moderated by pandemic-related caregiver depressive symptoms and household chaos; the protective association was maintained at high levels of caregiver depressive symptoms or household chaos, although the association diminished when these co-occurred. The protective association between prepandemic self-regulation and subsequent behavior problems suggests longitudinal benefits of preschoolers' inhibitory and emotional control. Despite reduced protection associated with co-occurring caregiver and household challenges, self-regulation continued to demonstrate protection against subsequent behavior problems, even in the midst of a pandemic.

Nonlinear combined harmonic resonances of composite cylindrical shells operating in hygro-thermo-electro-magneto-mechanical fields

By considering the effects of the hygro-thermo-electro-magnetic environments, von Karman nonlinear terms, and multi-harmonic excitations, a coupled nonlinear vibration modeling of composite cylindrical shells comprising a carbon nanotube-reinforced composite (CNTRC) core and two piezoelectric/magnetic composite (PEMC) skins is developed, and the nonlinear dynamic behaviors of such cylindrical shells under primary, super/sub-harmonic, and combined resonance states are investigated. In the theoretical modeling process, the effective mechanical properties of the CNTRC core are first determined using the mixing and Schapery laws, and the hygro-thermo-electro-magneto-mechanical constitutive relations of the PEMC skins are then formulated. Within the framework of Reissner-Mindlin shell theory, the Lagrangian of the system containing Green-Lagrange and von Karman nonlinear terms is derived, and solution techniques based on the multiscale method are provided to obtain nonlinear frequencies, dynamic responses, and phases of CNTRC-PEMC cylindrical shells under multi-physics fields. Consequently, comparison studies are conducted to validate the correctness of the proposed model from different aspects. Based on this, various resonance and chaos behaviors of such structures subjected to multiple load components are revealed and compared, and the influences of environmental factors and structure composition on the amplitude-frequency curves, time-history responses, and phase planes are explored, with several recommendations and findings being drawn.

Comparative Analysis of Nonlinear Dynamics of an Angular Velocity System of 2-DOF Aerial Manipulator with Different Physical Parameters

The two-degree-of-freedom (2-DOF) aerial manipulator is composed of a quadrotor aircraft and a 2-DOF manipulator, which significantly expands the scope of grabbing and transporting objects. After the manipulator is installed on the quadrotor, the manipulator and the load will cause serious interference to the quadrotor, resulting in difficulty of system control and even instability. This paper presents a mathematical model of the angular velocity system of the 2-DOF aerial manipulator. The model considers the influence of the manipulator and the load on the quadrotor. Based on this model, the nonlinear dynamics of the angular velocity system of the 2-DOF aerial manipulator are analyzed by solving the equilibrium points, calculating the Lyapunov exponents, analyzing the dynamic bifurcation diagram, and drawing the dynamic region distribution map. It is found that angular velocity can produce the dynamic behaviors of sink, period-doubling, and chaos under certain circumstances. By analyzing the nonlinear dynamic behaviors of the angular velocity system under different manipulator postures, different manipulator configurations, different load masses, and different load resistances, the stability of the angular velocity system is analyzed to guide the use of the aerial manipulator more safely and efficiently.

Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method

In recent years, newly proposed fractal-fractional calculus operators have been used to predict the chaotic behavior of some attractors, and the new operators can capture self-similarity in the studied chaotic attractors. The results of varying with fractal order and fractional order are interesting, however, the dynamics are barely analyzed in these studies, and the law of fractal order and fractional order on the system is not clear. In this paper, the fractal-fractional differential operators with inverse operator property are redefined in the Caputo sense, and a new numerical scheme is proposed based on the sixth-order Adomain decomposition method. Then the dynamics of the new multi-scroll Chen chaotic system and its three degradation modes are analyzed completely in the fractal-fractional sense. The influence of the change of fractal order and fractional order on the chaotic system is revealed. Finally, a new physical phenomenon of the fractal-fractional chaotic system is captured by observing the coexistence of multi-scroll and two-scroll chaotic attractors of the new system through a wood-grain-like attractor basin, as well as transient chaos, chaotic jumps, and complex state transition behaviors. It is shown that fractal-fractional multi-scroll Chen system has complex and specific dynamical behaviors.

Innovations in Computational Approaches for Nonlinear Problems and Complex System Simulations

Nonlinear problem solving and complex system simulation have become critical issues in many fields of science. The development of novel computational methods is crucial to understanding these complex systems. In this abstract, we explore the dynamic landscape of computational techniques, focusing on their uses in simulating complex systems and tackling nonlinear challenges. Creating complex algorithms that can deal with nonlinearity, chaos, and emergent behaviours is where it's at. Tools for modelling and comprehending such complex systems are few, but machine learning, artificial intelligence, and evolutionary computation are at the forefront. The way problems are solved has been completely rethought because of their nonlinearity-tolerance and ability to operate in high-dimensional domains. In addition, novel opportunities have arisen due to the combination of classical mathematical models with computer methods. The behaviour and emergent features of complex systems are best understood by hybrid approaches that combine differential equations, agent-based modelling, and cellular automata. These techniques provide a fine-grained comprehension of component interactions, illuminating emergent events. Moreover, the advent of high-performance computing has substantially expanded the breadth and resolution of simulations. Scientists are now able to probe increasingly complex systems, shedding light on their dynamics and behaviours. Computational capacities have been vastly improved by parallel computing, distributed systems, and cloud computing infrastructures, allowing for the study of systems that were once thought to be intractable. Nonlinear issues and complex system simulations can benefit greatly from the combination of cutting-edge computational approaches with domain-specific expertise. This abstract is a testament to the expanding significance and potential of these computational approaches in understanding complex systems and opening up new frontiers for research and solving problems.

Correlation of supersonic wind tunnel measurements with a nonlinear aeroelastic theoretical/computational model of a thin plate

Supersonic wind tunnel test data is compared with a nonlinear aeroelastic computational model, considering a freestream flow with Mach nearly 2, coupled cavity, and no-shock impingement. The measurements include Limit Cycle Oscillations (LCO) for the given set of flow and structural parameters. The effect of a static pressure differential, temperature differential, and the type of LCO is also studied: periodic or chaotic. A fully coupled aero-thermal–acoustic–elastic analysis was carried out, where the strong dependency of the dynamic instability upon the in-plane boundary stiffness was discovered. Associated with aerodynamic and acoustic formulations, the nonlinearities from the structure are found to be the strongest factor determining the occurrence and character of LCO. At the same time, the cavity effect was found to be negligible for this experimental configuration. Additionally, a comparison analysis was performed on the aerodynamic model for this flow condition between the Linear Piston Theory and the Full Potential Aerodynamics. The calculation of the critical flutter boundary was also performed in terms of the static pressure differential between the cavity pressure and the panel surface pressure, presenting regions where the panel is in static deformation due to the pressure differential versus LCO response. The comparison with the analytical model showed good agreement with the measured data, achieving a similar panel displacement at three-quarters of the panel length as well as the expected behavior of periodicity or chaos for specific values of temperature and static pressure differential.

Dynamical behavior of chaos, bifurcation analysis and soliton solutions to a Konno-Onno model.

The fractional coupled Konno-Onno model, which is frequently used in numerous fields of scientific and engineering disciplines, is being investigated in the current study in order to gain an understanding of complex phenomena and systems. The two main goals of this study are to be accomplished. Firstly, the research aims to identify novel solitons for the fractional coupled Konno-Onno model using the unified technique, which is currently absent from the literature. Secondly, a novel strategy that hasn't been previously investigated is phase portrait analysis for both perturbed and non-perturbed dynamical systems. The current study uses appropriate parametric values in phase plane analysis, 2D, 3D, and density plots to ensure the results are physically compatible. The results validate the claim that the technique used in this research to produce complete and uniform responses is not only simple to use and effective, but also substantially faster in computing. The technique is useful for resolving more complex phenomena that arise in engineering and mathematical physics.

New traveling solutions, phase portrait and chaotic pattern for the generalized (2+1)-dimensional nonlinear conformable fractional stochastic Schrödinger equations forced by multiplicative Brownian motion

The paper mainly studies the traveling wave solutions, phase portrait and chaotic pattern of the generalized fractional stochastic Schrödinger equations forced by multiplicative Brownian motion. By using the polynomial complete discrimination method, the hyperbolic functions, rational functions and Jacobi elliptic function solutions are obtained. Moreover, the physics properties of the obtained solutions are shown through three-dimensional, two-dimensional and contour graphs. In order to help better analyze dynamic behavior, phase diagrams, chaos behavior and sensitivity are plotted by using Maple software.

Temporality-induced chaos in the Kuramoto Model

Switched dynamical systems have been extensively studied in engineering literature in the context of system control. In these systems, the dynamical laws change between different subsystems depending on the environment, a process that is known to produce emergent behaviors---notably chaos. These dynamics are analogous to those of temporal networks, in which the network topology changes over time, thereby altering the dynamics on the network. It stands to reason that temporal networks may therefore produce emergent chaos and other exotic behaviors unanticipated in static networks, yet concrete examples remain elusive. Here, we present a minimal example of a networked system in which temporality produces chaotic dynamics not possible in any static subnetwork alone. Specifically, we consider a variant of the famous Kuramoto model, in which the network topology alternates between different configurations in response to the phase dynamics. We show under certain conditions this can produce a strange attractor, and we verify the presence of chaos by analyzing its geometrical properties. Our results provide new insights on the consequences of temporality for network dynamics, and acts as a proof of concept for a novel mechanism behind generating chaotic dynamics in networks.

Modified models of radiation pressure instability applied to 10, 105, and 107 M⊙ accreting black holes

Context. Some accreting black holes exhibit much stronger variability patterns than the usual stochastic variations. Radiation pressure instability is one of the proposed mechanisms that might account for this effect. Aims. We model luminosity changes for objects with a black hole mass of 10, 105, and 107 solar masses, using the time-dependent evolution of an accretion disk that is unstable as a result of the dominant radiation pressure. We concentrate on the outburst timescales. We explore the influence of the hot coronal flow above the cold disk, the inner purely hot flow, and the effect of the magnetic field on the time evolution of the disk-corona system. For intermediate-mass black holes and active galactic nuclei, we also explore the role of the disk outer radius because a disk that is fed by tidal disruption events (TDE) can be quite small. Methods. We used a 1D vertically integrated time-dependent numerical scheme that models the simultaneous evolution of the disk and corona, which is coupled by the vertical mass exchange. We parameterized the strength of the large-scale toroidal magnetic fields according to a local accretion rate. We also discuss a possible inner optically thin flow, the advection-dominated accretion flow (ADAF). This flow would require modification of the inner boundary condition of the cold disk flow. For the set of the global parameters, we calculated the variability timescales and outburst amplitudes of the disk and the corona. Results. We found that the role of the inner ADAF and the accreting corona are relatively unimportant, but the outburst character strongly depends on the magnetic field and on the outer radius of the disk if this radius is smaller (due to the TDE phenomenon) than the size of the instability zone in a stationary disk with infinite radius. For microquasars, the dependence on the magnetic field is monotonic, and the period decreases with the field strength. For higher black hole masses, the dependence is nonmonotonic, and an initial rise of the period is later replaced with a relatively rapid decrease as the magnetic field continues to rise. A still stronger magnetic field stabilizes the disk. When we assumed a smaller disk outer radiusfor 105 and 107 M⊙, the outbursts were shorter and led to complex multiscale outbursts for some parameters, thus approaching the behavior of deterministic chaos. Conclusions. Our computations confirm that the radiation pressure instability model can account for heartbeat states in microquasars. The rapid variability detected in intermediate-mass black holes in the form of quasi-periodic eruptions can be consistent with the model, but only when it is combined with the TDE phenomenon. The yearly repeating variability in changing-look active galactic nuclei in our model also requires a small outer radius either due to the recent TDE or due to the gap in the disk that is related to a secondary black hole.

Chaotic golden ratio guided local search for big data optimization

Biological systems where order arises from disorder inspires for many metaheuristic optimization techniques. Self-organization and evolution are the common behaviour of chaos and optimization algorithms. Chaos can be defined as an ordered state of disorder that is hypersensitive to initial conditions. Therefore, chaos can help create order out of disorder. In the scope of this work, Golden Ratio Guided Local Search method was improved with inspiration by chaos and named as Chaotic Golden Ratio Guided Local Search (CGRGLS). Chaos is used as a random number generator in the proposed method. The coefficient in the equation for determining adaptive step size was derived from the Singer Chaotic Map. Performance evaluation of the proposed method was done by using CGRGLS in the local search part of MLSHADE-SPA algorithm. The experimental studies carried out with the electroencephalographic signal decomposition-based optimization problems, named as Big Data optimization problem (Big-Opt), introduced at the Congress on Evolutionary Computing Big Data Competition (CEC’2015). Experimental results have shown that the local search method developed using chaotic maps has an effect that increases the performance of the algorithm.